论文标题
蠕动的惯性扭矩
Inertial torque on a squirmer
论文作者
论文摘要
在静态流体中沉降的小球体会经历一种惯性扭矩，使其对齐，因此首先与它的宽面定居。在这里，我们表明一个活跃的粒子也会经历这种扭矩，因为它在静止状态下沉淀在液体中。对于球形蠕动器，扭矩为$ \ boldsymbol {t}^\ prime = - {\ tfrac {9} {8}} {8}} m_f（\ boldsymbol {v} _s _s^_s^{（0）} \ wedge \ wedge \ boldsymbol $ \ boldsymbol {v} _s^{（0）} $是游泳速度，$ \ boldsymbol {v} _g^{（0）} $是stokes近似中的沉降速度，$ m_f $是等效的液体。这种扭矩使游泳方向与重力保持一致：游泳是稳定的，游泳是不稳定的。
A small spheroid settling in a quiescent fluid experiences an inertial torque that aligns it so that it settles with its broad side first. Here we show that an active particle experiences such a torque too, as it settles in a fluid at rest. For a spherical squirmer, the torque is $\boldsymbol{T}^\prime = -{\tfrac{9}{8}} m_f (\boldsymbol{v}_s^{(0)} \wedge \boldsymbol{v}_g^{(0)})$ where $\boldsymbol{v}_s^{(0)}$ is the swimming velocity, $\boldsymbol{v}_g^{(0)}$ is the settling velocity in the Stokes approximation, and $m_f$ is the equivalent fluid mass. This torque aligns the swimming direction against gravity: swimming up is stable, swimming down is unstable.
